You are Here: Home

Simplifying (an equation with a fraction within a fraction)

Announcements Posted on
Study Help needs new mods! 14-04-2014
Post on TSR and win a prize! Find out more... 10-04-2014
1. I find it difficult to simplify an equation which has a fraction within a fraction. For example, I do not understand how to simplify this:

Apparently, this can be rewritten as this:

But I do not understand the process used to achieve this. I would be grateful if someone could take me through the process of simplifying this equation and perhaps help me to understand a general method for simplifying equations involving a fraction within a fraction.
2. (Original post by Stikki)
I find it difficult to simplify an equation which has a fraction within a fraction. For example, I do not understand how to simplify this:

Apparently, this can be rewritten as this:

But I do not understand the process used to achieve this. I would be grateful if someone could take me through the process of simplifying this equation and perhaps help me to understand a general method for simplifying equations involving a fraction within a fraction.
If you multiply the entire fraction by (x+1)/(x+1) [which does not change the value since it is equal to 1] you find that the numerator becomes x+1 and the denominator becomes 1+x+1=x+2

Hence we can write it as
3. Another way is

Find a common denominator for the bottom

Simplify

Then just remembering division of fractions, 1 divided by a fraction is the same as 1 times the reciprocal.
4. take the denominator:

(1/(x+1)) + 1

you can multiply the 1 by (x+1)/(x+1) to make it:

(1/(x+1)) + (x+1)/(x+1)

now both fractions in the denominator have a common denominator of x+1, so turn it into one fraction:

(1/(x+1)) + (x+1)/(x+1) = (1+(x+1))/(x+1)

which simplifies to (x+2)/(x+1)

so the fraction is now 1/((x+2)/(x+1))

as i assume you know, you can take the denominator of the denominator and stick it on the numerator to turn this into:

(x+1)/(x+2)

voila
5. First you should simplify the denominator to get rid of that fraction there. So simplify 1/(1+x)+1.

Edit: or just do everything to poster above me did
6. do the smallest one frst, if that makes sense:

7. I understand how it works now. Thank you everyone.
8. (Original post by Prokaryotic_crap)
do the smallest one frst, if that makes sense:

Wouldn't it be better to times through by x+1 to begin as it can get confusing with remembering which line is more prevalent?
9. (Original post by Stikki)

Hence,

Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
your full birthday is required
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Updated: November 21, 2009
Study resources